a) Can the de nition of f(x) when x 6= 1 be simpli ed? If yes, what is the simpler expression?

Question 1. 3+5=8 marks
b) The equation x2  6x + y2 + 8y = 24 describes a circle.
i `Complete the square` to write the equation in form (x a)2 + (y  b)2 = r2
ii Write down the coordinates of the centre of the circle and its radius.
iii What are the coordinates of the uppermost point of the circle?
Question 2. 3+2+4+4=13 marks
Consider the function with piecewise de nition
a) Can the de nition of f(x) when x 6= 1 be simpli ed? If yes, what is the simpler expression?
b) Sketch the graph of f(x) carefully for x between -5 and 3.
c) What is the domain of this function? What is its range? Justify your answers.
d) Is f(x) continuous? Assess this property formally.
Question 9. 4+5+2=11 marks
A particle moves along a number line so that its position at time t is given by
s(t) = t3  10t2 + 12t (t  0)
where s is in centimetres and t in seconds.
a) When does the particle change direction ? (i.e. when does its velocity change from nega-
tive to positive or vice versa?)
b) When is the particle moving to the right?
c) What is the furthest left the particle attains?
total 90 marks
4


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